Is ${634572}$ divisible by $4$ ?
Solution: A number is divisible by $4$ if the last two digits are divisible by $4$ . [ Why? We can rewrite the number as a multiple of $100$ plus the last two digits: $ \gray{6345} {72} = \gray{6345} \gray{00} + {72} $ Because $634500$ is a multiple of $100$ , it is also a multiple of $4$ So as long as the value of the last two digits, ${72}$ , is divisible by $4$ , the original number must also be divisible by $4$ Is the value of the last two digits, $72$ , divisible by $4$ Yes, ${72 \div 4 = 18}$, so $634572$ must also be divisible by $4$.